Learning functional connectivity (FC) network from resting-state function magnetic resonance imaging (RS-fMRI) data via sparse representation (SR) or weighted SR (WSR) has been proved to be promising for the diagnosis of Alzheimer's disease and its prodromal stage, mild cognitive impairment (MCI). However, traditional SR/WSR based approaches learn the representation of each brain region independently, without fully taking into account the possible relationship between brain regions. To remedy this limitation, we propose a novel FC modeling approach by considering two types of possible relationship between different brain regions which are incorporated into SR/WSR approaches in the form of regularization. In this way, the representations of all brain regions can be jointly learned. Furthermore, an efficient alternating optimization algorithm is also developed to solve the resulting model. Experimental results show that our proposed method not only outperforms SR and WSR in the diagnosis of MCI subjects, but also leads to the brain FC network with better modularity structure.